Pith Number

pith:TZF4HZJP

pith:2003:TZF4HZJPRGQKKTI4BOHCF3YTPR

not attested not anchored not stored refs pending

Sparse Graph Codes for Quantum Error-Correction

David J.C. MacKay, Graeme Mitchison, Paul L. McFadden

arxiv:quant-ph/0304161 v3 · 2003-04-24 · quant-ph

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TZF4HZJPRGQKKTI4BOHCF3YTPR}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T00:58:26.350922Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e4bc3e52f89a0a54d1c0b8e22ef137c520cff5d2121bf2a7596c1824ab24045

Aliases

arxiv: quant-ph/0304161 · arxiv_version: quant-ph/0304161v3 · doi: 10.48550/arxiv.quant-ph/0304161 · pith_short_12: TZF4HZJPRGQK · pith_short_16: TZF4HZJPRGQKKTI4 · pith_short_8: TZF4HZJP

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/TZF4HZJPRGQKKTI4BOHCF3YTPR \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 9e4bc3e52f89a0a54d1c0b8e22ef137c520cff5d2121bf2a7596c1824ab24045

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "303457d021ba730f96cf6a44b93632e5e3aeeff136fb353cb5e479ee3f12c60e",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "quant-ph",
    "submitted_at": "2003-04-24T21:20:34Z",
    "title_canon_sha256": "2a6513296d7b69d21f7e62f5b270698defc25ead628791171cf3f8ed0117f824"
  },
  "schema_version": "1.0",
  "source": {
    "id": "quant-ph/0304161",
    "kind": "arxiv",
    "version": 3
  }
}